Koopmans-tuned Heyd-Scuseria-Ernzerhof hybrid functional calculations of acceptors in GaN

The Heyd-Scuseria-Ernzerhof (HSE) hybrid functional has become a widely used tool for theoretical calculations of point defects in semiconductors. It generally offers a satisfactory qualitative description of defect properties, including the donor/acceptor nature of defects, lowest energy charge states, thermodynamic and optical transition levels, Franck-Condon shifts, photoluminescence (PL) band shapes, and carrier capture cross sections. However, there are noticeable quantitative discrepancies in these properties when compared to experimental results. Some of these discrepancies arise from the presence of self-interaction in various parametrizations of the HSE. Other errors are due to the use of the periodic boundary conditions. In this study, we demonstrate that the error correction scheme based on extrapolation to the dilute limit effectively eliminates the errors due to artificial electrostatic interactions of periodic images and interactions due to the defect state delocalization. This yields parametrizations of HSE that satisfy the generalized Koopmans' condition, essentially eliminating self-interaction from defect state orbitals. We apply this HSE Koopmans tuning individually to a range of cation site acceptors in GaN (${\mathrm{Be}}_{\mathrm{Ga}}, {\mathrm{Mg}}_{\mathrm{Ga}}, {\mathrm{Zn}}_{\mathrm{Ga}}, {\mathrm{Ca}}_{\mathrm{Ga}}, {\mathrm{Cd}}_{\mathrm{Ga}}$, and ${\mathrm{Hg}}_{\mathrm{Ga}}$) and compare the HSE results with experimental data from PL spectra. The Koopmans-compliant HSE calculations show a significantly improved quantitative agreement with the experiment.